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A133161 Indices of the triangular numbers which are also centered triangular number. 2
1, 4, 16, 61, 229, 856, 3196, 11929, 44521, 166156, 620104, 2314261, 8636941, 32233504, 120297076, 448954801, 1675522129, 6253133716, 23337012736, 87094917229, 325042656181, 1213075707496, 4527260173804, 16895964987721 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also, indices of the triangular numbers which are sums of three consecutive triangular numbers (see A129803).

LINKS

Table of n, a(n) for n=1..24.

A. Kozikowska, Topological classes of statically determinate beams with arbitrary number of supports, JOURNAL OF THEORETICAL AND APPLIED MECHANICS 49, 4, pp. 1079-1100, Warsaw 2011; (see Eq. 5.18). - N. J. A. Sloane, Dec 17 2011.

Index entries for linear recurrences with constant coefficients, signature (5,-5,1).

FORMULA

a(n+2)=4*a(n+1)-a(n)+1.

a(n+1)=2*a(n)+0.5+0.5*(12*a(n)^2+12*a(n)-15)^0.5.

G.f.: x*(1-x+x^2)/(1-x)/(1-4*x+x^2). - R. J. Mathar, Oct 24 2007

a(n)=-(1/2)-(1/4)*sqrt(3)*[2-sqrt(3)]^n+(1/4)*sqrt(3)*[2+sqrt(3)]^n+(3/4)*[2-sqrt(3)]^n+(3/4) *[2+sqrt(3)]^n, with n>=0 - Paolo P. Lava, Jul 30 2008

a(n)-a(n-1)= A005320(n-1). - R. J. Mathar, Mar 14 2016

MATHEMATICA

LinearRecurrence[{5, -5, 1}, {1, 4, 16}, 30] (* Harvey P. Dale, Aug 29 2017 *)

CROSSREFS

Cf. A001834, A102871, A128862, A129803, A001571.

Sequence in context: A203153 A126929 A268452 * A103820 A206570 A206790

Adjacent sequences:  A133158 A133159 A133160 * A133162 A133163 A133164

KEYWORD

nonn,easy

AUTHOR

Richard Choulet, Oct 09 2007

STATUS

approved

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Last modified August 16 00:25 EDT 2018. Contains 313782 sequences. (Running on oeis4.)